src/Tests/Tetrahedron.hs

   1 module Tests.Tetrahedron
   2 where
   3
   4 import Test.Framework (Test, testGroup)
   5 import Test.Framework.Providers.HUnit (testCase)
   6 import Test.HUnit
   7 import Test.QuickCheck (Property, (==>))
   8
   9 import Cardinal
  10 import Comparisons
  11 import FunctionValues
  12 import Tests.FunctionValues()
  13 import Tetrahedron
  14 import ThreeDimensional
  15
  16 -- HUnit Tests
  17
  18
  19 -- | Check the volume of a particular tetrahedron (computed by hand)
  20 --   and whether or not it contains a specific point chosen to be
  21 --   outside of it. Its vertices are in clockwise order, so the volume
  22 --   should be negative.
  23 tetrahedron1_geometry_tests :: Test.Framework.Test
  24 tetrahedron1_geometry_tests =
  25   testGroup "tetrahedron1 geometry"
  26               [ testCase "volume1" volume1,
  27                 testCase "doesn't contain point1" doesnt_contain_point1]
  28   where
  29     p0 = (0, -0.5, 0)
  30     p1 = (0, 0.5, 0)
  31     p2 = (2, 0, 0)
  32     p3 = (1, 0, 1)
  33     t = Tetrahedron { v0 = p0,
  34                       v1 = p1,
  35                       v2 = p2,
  36                       v3 = p3,
  37                       fv = empty_values,
  38                       precomputed_volume = 0 }
  39
  40     volume1 :: Assertion
  41     volume1 =
  42       assertEqual "volume is correct" True (vol ~= (-1/3))
  43       where
  44         vol = volume t
  45
  46     doesnt_contain_point1 :: Assertion
  47     doesnt_contain_point1 =
  48       assertEqual "doesn't contain an exterior point" False contained
  49       where
  50         exterior_point = (5, 2, -9.0212)
  51         contained = contains_point t exterior_point
  52
  53
  54 -- | Check the volume of a particular tetrahedron (computed by hand)
  55 --   and whether or not it contains a specific point chosen to be
  56 --   inside of it. Its vertices are in counter-clockwise order, so the
  57 --   volume should be positive.
  58 tetrahedron2_geometry_tests :: Test.Framework.Test
  59 tetrahedron2_geometry_tests =
  60   testGroup "tetrahedron2 geometry"
  61               [ testCase "volume1" volume1,
  62                 testCase "contains point1" contains_point1]
  63   where
  64     p0 = (0, -0.5, 0)
  65     p1 = (2, 0, 0)
  66     p2 = (0, 0.5, 0)
  67     p3 = (1, 0, 1)
  68     t = Tetrahedron { v0 = p0,
  69                       v1 = p1,
  70                       v2 = p2,
  71                       v3 = p3,
  72                       fv = empty_values,
  73                       precomputed_volume = 0 }
  74
  75     volume1 :: Assertion
  76     volume1 = assertEqual "volume1 is correct" True (vol ~= (1/3))
  77       where
  78         vol = volume t
  79
  80     contains_point1 :: Assertion
  81     contains_point1 = assertEqual "contains an inner point" True contained
  82         where
  83           inner_point = (1, 0, 0.5)
  84           contained = contains_point t inner_point
  85
  86
  87 -- | Ensure that tetrahedra do not contain a particular point chosen to
  88 --   be outside of them.
  89 containment_tests :: Test.Framework.Test
  90 containment_tests =
  91   testGroup "containment tests"
  92               [ testCase "doesn't contain point2" doesnt_contain_point2,
  93                 testCase "doesn't contain point3" doesnt_contain_point3,
  94                 testCase "doesn't contain point4" doesnt_contain_point4,
  95                 testCase "doesn't contain point5" doesnt_contain_point5]
  96   where
  97     p2 = (0.5, 0.5, 1)
  98     p3 = (0.5, 0.5, 0.5)
  99     exterior_point = (0, 0, 0)
 100
 101     doesnt_contain_point2 :: Assertion
 102     doesnt_contain_point2 =
 103       assertEqual "doesn't contain an exterior point" False contained
 104       where
 105         p0 = (0, 1, 1)
 106         p1 = (1, 1, 1)
 107         t = Tetrahedron { v0 = p0,
 108                           v1 = p1,
 109                           v2 = p2,
 110                           v3 = p3,
 111                           fv = empty_values,
 112                           precomputed_volume = 0 }
 113         contained = contains_point t exterior_point
 114
 115
 116     doesnt_contain_point3 :: Assertion
 117     doesnt_contain_point3 =
 118       assertEqual "doesn't contain an exterior point" False contained
 119       where
 120         p0 = (1, 1, 1)
 121         p1 = (1, 0, 1)
 122         t = Tetrahedron { v0 = p0,
 123                           v1 = p1,
 124                           v2 = p2,
 125                           v3 = p3,
 126                           fv = empty_values,
 127                           precomputed_volume = 0 }
 128         contained = contains_point t exterior_point
 129
 130
 131     doesnt_contain_point4 :: Assertion
 132     doesnt_contain_point4 =
 133       assertEqual "doesn't contain an exterior point" False contained
 134       where
 135         p0 = (1, 0, 1)
 136         p1 = (0, 0, 1)
 137         t = Tetrahedron { v0 = p0,
 138                           v1 = p1,
 139                           v2 = p2,
 140                           v3 = p3,
 141                           fv = empty_values,
 142                           precomputed_volume = 0 }
 143         contained = contains_point t exterior_point
 144
 145
 146     doesnt_contain_point5 :: Assertion
 147     doesnt_contain_point5 =
 148       assertEqual "doesn't contain an exterior point" False contained
 149       where
 150         p0 = (0, 0, 1)
 151         p1 = (0, 1, 1)
 152         t = Tetrahedron { v0 = p0,
 153                           v1 = p1,
 154                           v2 = p2,
 155                           v3 = p3,
 156                           fv = empty_values,
 157                           precomputed_volume = 0 }
 158         contained = contains_point t exterior_point
 159
 160
 161 -- | The barycentric coordinate of v0 with respect to itself should
 162 --   be one.
 163 prop_b0_v0_always_unity :: Tetrahedron -> Property
 164 prop_b0_v0_always_unity t =
 165     (volume t) > 0 ==> (b0 t) (v0 t) ~= 1.0
 166
 167 -- | The barycentric coordinate of v1 with respect to v0 should
 168 --   be zero.
 169 prop_b0_v1_always_zero :: Tetrahedron -> Property
 170 prop_b0_v1_always_zero t =
 171     (volume t) > 0 ==> (b0 t) (v1 t) ~= 0
 172
 173 -- | The barycentric coordinate of v2 with respect to v0 should
 174 --   be zero.
 175 prop_b0_v2_always_zero :: Tetrahedron -> Property
 176 prop_b0_v2_always_zero t =
 177     (volume t) > 0 ==> (b0 t) (v2 t) ~= 0
 178
 179 -- | The barycentric coordinate of v3 with respect to v0 should
 180 --   be zero.
 181 prop_b0_v3_always_zero :: Tetrahedron -> Property
 182 prop_b0_v3_always_zero t =
 183     (volume t) > 0 ==> (b0 t) (v3 t) ~= 0
 184
 185 -- | The barycentric coordinate of v1 with respect to itself should
 186 --   be one.
 187 prop_b1_v1_always_unity :: Tetrahedron -> Property
 188 prop_b1_v1_always_unity t =
 189     (volume t) > 0 ==> (b1 t) (v1 t) ~= 1.0
 190
 191 -- | The barycentric coordinate of v0 with respect to v1 should
 192 --   be zero.
 193 prop_b1_v0_always_zero :: Tetrahedron -> Property
 194 prop_b1_v0_always_zero t =
 195     (volume t) > 0 ==> (b1 t) (v0 t) ~= 0
 196
 197 -- | The barycentric coordinate of v2 with respect to v1 should
 198 --   be zero.
 199 prop_b1_v2_always_zero :: Tetrahedron -> Property
 200 prop_b1_v2_always_zero t =
 201     (volume t) > 0 ==> (b1 t) (v2 t) ~= 0
 202
 203 -- | The barycentric coordinate of v3 with respect to v1 should
 204 --   be zero.
 205 prop_b1_v3_always_zero :: Tetrahedron -> Property
 206 prop_b1_v3_always_zero t =
 207     (volume t) > 0 ==> (b1 t) (v3 t) ~= 0
 208
 209 -- | The barycentric coordinate of v2 with respect to itself should
 210 --   be one.
 211 prop_b2_v2_always_unity :: Tetrahedron -> Property
 212 prop_b2_v2_always_unity t =
 213     (volume t) > 0 ==> (b2 t) (v2 t) ~= 1.0
 214
 215 -- | The barycentric coordinate of v0 with respect to v2 should
 216 --   be zero.
 217 prop_b2_v0_always_zero :: Tetrahedron -> Property
 218 prop_b2_v0_always_zero t =
 219     (volume t) > 0 ==> (b2 t) (v0 t) ~= 0
 220
 221 -- | The barycentric coordinate of v1 with respect to v2 should
 222 --   be zero.
 223 prop_b2_v1_always_zero :: Tetrahedron -> Property
 224 prop_b2_v1_always_zero t =
 225     (volume t) > 0 ==> (b2 t) (v1 t) ~= 0
 226
 227 -- | The barycentric coordinate of v3 with respect to v2 should
 228 --   be zero.
 229 prop_b2_v3_always_zero :: Tetrahedron -> Property
 230 prop_b2_v3_always_zero t =
 231     (volume t) > 0 ==> (b2 t) (v3 t) ~= 0
 232
 233 -- | The barycentric coordinate of v3 with respect to itself should
 234 --   be one.
 235 prop_b3_v3_always_unity :: Tetrahedron -> Property
 236 prop_b3_v3_always_unity t =
 237     (volume t) > 0 ==> (b3 t) (v3 t) ~= 1.0
 238
 239 -- | The barycentric coordinate of v0 with respect to v3 should
 240 --   be zero.
 241 prop_b3_v0_always_zero :: Tetrahedron -> Property
 242 prop_b3_v0_always_zero t =
 243     (volume t) > 0 ==> (b3 t) (v0 t) ~= 0
 244
 245 -- | The barycentric coordinate of v1 with respect to v3 should
 246 --   be zero.
 247 prop_b3_v1_always_zero :: Tetrahedron -> Property
 248 prop_b3_v1_always_zero t =
 249     (volume t) > 0 ==> (b3 t) (v1 t) ~= 0
 250
 251 -- | The barycentric coordinate of v2 with respect to v3 should
 252 --   be zero.
 253 prop_b3_v2_always_zero :: Tetrahedron -> Property
 254 prop_b3_v2_always_zero t =
 255     (volume t) > 0 ==> (b3 t) (v2 t) ~= 0
 256
 257
 258 -- | Used for convenience in the next few tests; not a test itself.
 259 p :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
 260 p t i j k l = (polynomial t) (xi t i j k l)
 261
 262 -- | Given in Sorokina and Zeilfelder, p. 78.
 263 prop_c3000_identity :: Tetrahedron -> Property
 264 prop_c3000_identity t =
 265     (volume t) > 0 ==>
 266                c t 3 0 0 0 ~= p t 3 0 0 0
 267
 268 -- | Given in Sorokina and Zeilfelder, p. 78.
 269 prop_c2100_identity :: Tetrahedron -> Property
 270 prop_c2100_identity t =
 271     (volume t) > 0 ==>
 272       c t 2 1 0 0 ~= (term1 - term2 + term3 - term4)
 273         where
 274           term1 = (1/3)*(p t 0 3 0 0)
 275           term2 = (5/6)*(p t 3 0 0 0)
 276           term3 = 3*(p t 2 1 0 0)
 277           term4 = (3/2)*(p t 1 2 0 0)
 278
 279 -- | Given in Sorokina and Zeilfelder, p. 78.
 280 prop_c1110_identity :: Tetrahedron -> Property
 281 prop_c1110_identity t =
 282     (volume t) > 0 ==>
 283        c t 1 1 1 0 ~= (term1 + term2 - term3 - term4)
 284         where
 285           term1 = (1/3)*((p t 3 0 0 0) + (p t 0 3 0 0) + (p t 0 0 3 0))
 286           term2 = (9/2)*(p t 1 1 1 0)
 287           term3 = (3/4)*((p t 2 1 0 0) + (p t 1 2 0 0) + (p t 2 0 1 0))
 288           term4 = (3/4)*((p t 1 0 2 0) + (p t 0 2 1 0) + (p t 0 1 2 0))
 289
 290 prop_x_rotation_doesnt_affect_front :: Tetrahedron -> Bool
 291 prop_x_rotation_doesnt_affect_front t =
 292     expr1 == expr2
 293     where
 294       fv0 = Tetrahedron.fv t
 295       fv1 = rotate cwx (Tetrahedron.fv t)
 296       expr1 = front fv0
 297       expr2 = front fv1
 298
 299 prop_x_rotation_doesnt_affect_back :: Tetrahedron -> Bool
 300 prop_x_rotation_doesnt_affect_back t =
 301     expr1 == expr2
 302     where
 303       fv0 = Tetrahedron.fv t
 304       fv1 = rotate cwx (Tetrahedron.fv t)
 305       expr1 = back fv0
 306       expr2 = back fv1
 307
 308
 309 prop_y_rotation_doesnt_affect_left :: Tetrahedron -> Bool
 310 prop_y_rotation_doesnt_affect_left t =
 311     expr1 == expr2
 312     where
 313       fv0 = Tetrahedron.fv t
 314       fv1 = rotate cwy (Tetrahedron.fv t)
 315       expr1 = left fv0
 316       expr2 = left fv1
 317
 318 prop_y_rotation_doesnt_affect_right :: Tetrahedron -> Bool
 319 prop_y_rotation_doesnt_affect_right t =
 320     expr1 == expr2
 321     where
 322       fv0 = Tetrahedron.fv t
 323       fv1 = rotate cwy (Tetrahedron.fv t)
 324       expr1 = right fv0
 325       expr2 = right fv1
 326
 327
 328 prop_z_rotation_doesnt_affect_down :: Tetrahedron -> Bool
 329 prop_z_rotation_doesnt_affect_down t =
 330     expr1 == expr2
 331     where
 332       fv0 = Tetrahedron.fv t
 333       fv1 = rotate cwz (Tetrahedron.fv t)
 334       expr1 = down fv0
 335       expr2 = down fv1
 336
 337
 338 prop_z_rotation_doesnt_affect_top :: Tetrahedron -> Bool
 339 prop_z_rotation_doesnt_affect_top t =
 340     expr1 == expr2
 341     where
 342       fv0 = Tetrahedron.fv t
 343       fv1 = rotate cwz (Tetrahedron.fv t)
 344       expr1 = top fv0
 345       expr2 = top fv1
 346
 347 prop_swapping_vertices_doesnt_affect_coefficients1 :: Tetrahedron -> Bool
 348 prop_swapping_vertices_doesnt_affect_coefficients1 t =
 349       c t 0 0 1 2 == c t' 0 0 1 2
 350         where
 351           t' = t { v0 = (v1 t), v1 = (v0 t) }
 352
 353 prop_swapping_vertices_doesnt_affect_coefficients2 :: Tetrahedron -> Bool
 354 prop_swapping_vertices_doesnt_affect_coefficients2 t =
 355       c t 0 1 1 1 == c t' 0 1 1 1
 356         where
 357           t' = t { v2 = (v3 t), v3 = (v2 t) }
 358
 359 prop_swapping_vertices_doesnt_affect_coefficients3 :: Tetrahedron -> Bool
 360 prop_swapping_vertices_doesnt_affect_coefficients3 t =
 361       c t 2 1 0 0 == c t' 2 1 0 0
 362         where
 363           t' = t { v2 = (v3 t), v3 = (v2 t) }
 364
 365 prop_swapping_vertices_doesnt_affect_coefficients4 :: Tetrahedron -> Bool
 366 prop_swapping_vertices_doesnt_affect_coefficients4 t =
 367       c t 2 0 0 1 == c t' 2 0 0 1
 368         where
 369           t' = t { v0 = (v3 t), v3 = (v0 t) }